A proof of the generalized Nakayama conjecture for algebras with \(J^{2l+1}=0\) and \(A/J^ l\) representation finite
type: Item
instance of: scholarly article
title: A proof of the generalized Nakayama conjecture for algebras with \(J^{2l+1}=0\) and \(A/J^ l\) representation finite
zbMATH Open document ID: 0794.16007
DOI: 10.1016/0022-4049(92)90093-U
author: Peter Dräxler
author: Dieter Happel
published in: Journal of Pure and Applied Algebra
publication date: 1992-09-27T00:00:00Z
review text: Let \(A\) be a finite dimensional algebra over a field \(k\). The generalized Nakayama conjecture states \(\text{Ext}_ A^ i (\Hom_ k(A,k),S)\neq 0\) for each simple \(A\)-module \(S\) and some \(i\geq 0\). A more general version is known if \(J(A)^ 3=0\) [\textit{E. L. Green} and \textit{B. Zimmermann- Huisgen}, Math. Z. 206, No. 4, 505-526 (1991; Zbl 0707.16002)]. Here the authors give a short proof under the assumption that there exists a natural number \(t\) such that \(J(A)^{2t+1}=0\) and \(A/J(A)^ t\) is representation finite.
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 60681
zbMATH Keywords: finistic dimension
zbMATH Keywords: minimal injection resolution
zbMATH Keywords: finite dimensional algebra
zbMATH Keywords: generalized Nakayama conjecture
zbMATH Keywords: representation finite
Wikidata QID: Q122877753
MaRDI profile type: Publication
cites work: On a Generalized Version of the Nakayama Conjecture
cites work: Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
cites work: Finitistic dimension of Artinian rings with vanishing radical cube
cites work: The Classification of Algebras by Dominant Dimension
cites work: On algebras with complete homology
description: scientific article; zbMATH DE number 60681